if you are moving with a big firm then they should do it all for you - wasn't it the accountants that came up with the so called balance sheet approach in the first place? Take your net Aussie salary, deduct from it an amount to cover housing in Aus, times this by COL from Aus to Singapore (roughly 1.5X if you're moving from Sydney), add on a housing allowance here plus, depending on the company, other benefits such as flights home (cash or kind), schooling, perhaps car allowance etc. Gross this up for Singapore tax and you are away.
E.g. you earn A$150,000. After tax this is approx $90,000 (say). Take off say $20K for housing = $70,000 multiply the result by 1.5 (105), add housing (depending on family size 5-10K per month, say $5 for these purposes) = 165, plus flights, say $10K if there are two of you, plus schools, say $20K, car say $30K = approx $230K, gross up is approx. $.270
Clearly to the extent your employer either pays you net, or pays for housing direct, provides a car etc. then you need to adjust this figure. You may also want to try and get a pay rise for coming but this sometimes isn't easy!
BTW, don't think if you end up with less than this you are being screwed, you aren't. Many organisations only cost of living adjust the "goods and services" part of your pay, not the part they hypothetically allocate to savings, which is sort of fair enough.
Come on, your an accountant, you can figure it out!